Harmonic vibrations of nanosized magnetoelectric bodies with coupled surface and interphase effects: Mathematical models and finite element approaches

The harmonic problems for piezomagnetoelectric nanosized bodies with taking into account the coupled damping and surface effects are considered on the base of the generalized Gurtin-Murdoch model. In the development of previous investigations, the coupled mechanical, electric and magnetic surface effects with surface inertial terms are introduced into the model. For a homogeneous model, the composite material is considered as homogeneous with the suitable effective material properties. The weak or generalized formulation of the steady-state oscillation problem is given together with the suitable formulation of the modal problem. For numerical solution of these problems, the finite element approximations, leading to a symmetric structure of finite element matrices, are present. The procedures of homogenization of piezomagnetoelectric nanostructured composite materials with piezoelectric and piezomagnetic phases are described on the base of the methods of effective moduli and finite elements

Mathematical models and finite element approaches for nanosized piezoelectric bodies with uncoulped and coupled surface effects

In this chapter the dynamic problems for piezoelectric nanosized bodies with account for coupled damping and surface effects are considered. For these problems we propose new mathematical model which generalizes the models of the elastic medium with damping in sense of the Rayleigh approach and with surface effects for the cases of piezoelectric materials. Our model of attenuation and surface effects has coupling properties between mechanical and electric fields, both for the damping terms and constitutive equations for piezoelectric materials on the surface. For solving the problems stated the finite element approximations are discussed. A set of effective finite element schemes is examined for finding numerical solutions of week statements for nonstationary problems, steady-state oscillation problems, modal problems and static problems within the framework of modelling of piezoelectric nanosized materials with damping and surface effects. For transient and harmonic problems, we demonstrate that the proposed models allow the use of the mode superposition method. In addition, we note that for transient and static problems we can use efficient finite element algorithms for solving the systems of linear algebraic equations with symmetric quasi-definite matrices both in the case of uncoupled surface effects and in the case of coupled surface effects

Finite Element Investigation of Effective Moduli of Transversely Isotropic Thermoelastic Materials with Nanoscale Porosity

Using the methods of effective moduli and finite elements, the effective properties of nanoporous thermoelastic transversely isotropic materials were studied for simple random and for closed structures of porosity. Nanoscale effects were modelled in the framework of the Gurtin-Murdoch model of interface stresses and of the high conductivity model. The modelling and solution of homogenization problems was performed in the ANSYS package, while structures of representative volumes with closed porosity were created in the ACELAN-COMPOS package. The effect of porosity, types of representative volumes and pore sizes on the values of the effective modules of nanoporous titanium is analysed. © 2020, Springer Nature Switzerland AG

Homogenization of Dispersion-Strengthened Thermoelastic Composites with Imperfect Interfaces by Using Finite Element Technique

The paper describes the homogenization procedure for a two-phase mixture composite that consists of two isotropic thermoelastic materials. It is assumed that the special interface conditions are held on the boundary between the phases, where the stress and the thermal flux jump over the interphase boundary are equal to the surface stresses and thermal flux at the interface. Such boundary conditions are used to describe the nanoscale effects in thermoelastic nanodimensional bodies and nanocomposites. The homogenization problems are solved using the approach of the effective moduli method, the finite element method and the algorithm for generating the representative volume of cubic finite elements with random distribution of element material properties. As a numerical example, a mixture wolfram-copper composite is considered, where the interface conditions are simulated by surface membrane and thermal shell elements

Finite element study of ceramic matrix piezocomposites with mechanical interface properties by the effective moduli method with different types of boundary Conditions

The paper deals with the problem of finding the effective moduli of a ceramic matrix composite with surface stresses on the interphase boundaries. The composite consists of a PZT ceramic matrix, elastic inclusions and interface boundaries. It is assumed that the interface stresses depend on the surface strains according to the Gurtin-Murdoch model. This model describes the size effects and contributes to the total stress-strain state only for nanodimensional inclusions. The homogenization problem was set and solved with the help of the effective moduli method for piezoelectric composites with interface boundaries and finite-element technologies used for simulating the representative volumes and solving the resulting boundary-value electroelastic problems. Here in the effective moduli method, different combinations of linear first-kind boundary conditions and constant second-kind boundary conditions for mechanical and electric fields were considered. The representative volume consisted of cubic finite elements with the material properties of the matrix or inclusions and also included the surface elements on the interfaces. Bulk elements were supplied with the material properties of the matrix or inclusions, using a simple random method. In the numerical example, the influence of the fraction of inclusions, the interface stresses and boundary conditions on the effective electroelastic modules were analysed